Forces applied to an instrument tip of a surgical robot can be estimated by measuring the reaction forces at the drape plate and the trocar. Friction, however, occurs at the rubber packing inside the trocar. The friction deteriorates estimation of the force applied to the instrument tip in the axial direction. This paper proposes a method to improve the accuracy of force estimation by designing a 1-DOF force sensor at the drape plate and measuring the friction that occurs in the rubber packing. Rectangular parallelepiped connectors between the upper and lower sections of the drape plate are designed to concentrate the strain from the reaction force within the drape plate. The proposed drape plate sensor can measure the reaction force accurately regardless of friction due to surface contact with the upper slide because the reaction force is measured within the internal structure of the drape plate. The sensor measures the reaction force in the axial direction with an error of 3.28 %. It is possible to estimate the axial force applied to the instrument tip with error of 8.26 % by measuring both the reaction force at the drape plate sensor and the friction within the rubber packing.